7.14.11 problem 11

Internal problem ID [436]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.2 (Series solution near ordinary points). Problems at page 216
Problem number : 11
Date solved : Monday, January 27, 2025 at 02:53:38 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 y^{\prime \prime }-2 x y^{\prime }+10 y&=0 \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

Order:=6; 
dsolve(5*diff(y(x),x$2)-2*x*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (1-x^{2}+\frac {1}{10} x^{4}\right ) y \left (0\right )+\left (\frac {4}{375} x^{5}-\frac {4}{15} x^{3}+x \right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 40

AsymptoticDSolveValue[5*D[y[x],{x,2}]-2*x*D[y[x],x]+10*y[x]==0,y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_2 \left (\frac {4 x^5}{375}-\frac {4 x^3}{15}+x\right )+c_1 \left (\frac {x^4}{10}-x^2+1\right ) \]